Abstract The problem of variable selection is a crucial and difficult aspect of statisticai modeling. Choosing the wrong predictor variables for the final model can result in either underfitting or overfitting. It is crucial to control the rate of false discovery during the inference stage, in variable selection methods. A false discovery rate is said in proportion to auxiliary variables that are improperly chosen among all selected variables. False discovery rate control has been studied for a long time, and several approaches have been developed to achieve an optimal solution. Recently, a new family of FDR control methods called “Knockoff filters” has been introduced. This thesis addresses the issue of variable selection in regression models error false discovery rate control whit various knockoff versions, including fixed-X knockoffs and X-model knockoffs. These knockoff methods can be suitable structures to imitate the existing variables and control the false discovery rate to acceptable limits. The performance of each type of knockoff method will be reviewed in comparison whit each other and some common methods to control the false discovery rate. The efficiency of the presented models has been studied using the data obtained from the simulation.       Keywords: variable selection, sparse regression, knockoff filter, false discovery rate.   

   Comparative comparison of performance evaluation models of agricultural and livestock companies in Kermanshah province and presentation of optimal performance evaluation model Abstract Objective: The evaluation process is one of the most important processes that every collection needs to ensure its survival and to know the quality of its performance and accurate implementation of its programs. In this regard, the current research was conducted with the aim of comparative comparison of performance evaluation models and providing the optimal performance evaluation model. Research Methodology: The research was conducted with a qualitative and documentary method. In order to achieve the objectives of the research, first by studying the selected texts and document review of researches related to common performance evaluation models, the main indicators and components intended to evaluate the performance of organizations and companies were categorized, then for each of the performance evaluation models, the indicators and components of that model It was evaluated and compiled, and finally, based on the obtained indicators, performance evaluation models were compared. Data analysis methods were thematic analysis and descriptive statistical indicators. Results: The results obtained from the research showed that among the performance evaluation models, the balanced evaluation model is a more comprehensive and optimal model and provides more complete results and more components for a comprehensive and correct evaluation of the performance of companies and organizations compared to other models. Conclusion: According to the obtained results, it can be said that among the performance evaluation models, the balanced evaluation model is the most optimal and efficient model for performance evaluation in agricultural and animal husbandry companies. Keywords: performance evaluation, Balanced Score Card, comparative comparison

Unemployment is one of the most important issues in all countries around the world. An increase in the number of unemployed in any society will cause a lot of problems. So having deep and appropriate knowledge of the factors affecting unemployment is taken into account to reduce it. In this thesis, we gathered data of Population and Housing census 2016 from the Statistical Center of Iran. These data categorized the active and unemployed population of 15 years old or above, based on gender and different levels of education in the counties of Iran. We edit these data, based on our purpose. Our purpose in the thesis is spatial modeling of the number of unemployed based on gender and education as covariates. To achieve this goal, we use Bayesian approach and a method called “integrated nested Laplace approximation” or INLA for short. For many years, Bayesian inference has relied upon Markov chain Monte Carlo (MCMC) methods. This approach focuses on estimating the joint posterior distribution of model parameters, therefore, it is computationally expensive in high-dimensional spaces. Instead, Inla focuses on estimating marginal posterior distributions, and according to tremendous developments in computational systems in recent years, it is done more quickly. In addition, INLA is expressed in models with GMRF feature and it has some advantages that reduce the time of model fitting calculations. Finally and after appropriate modeling of the data, we interpret the effects of the two variables of gender and education as well as spatial effects of the counties of Iran on the number of unemployed.

يكي از عوامل مهم در بررسي آموزش، پيش‌بيني پيشرفت ‌تحصيلي است و استفاده از فنون داده‌كاوي يكي از راه‌كار‌هاي نوين پيش‌بيني پيشرفت ‌تحصيلي است. در اين پايان‌نامه، فنون داده‌كاوي در دو بخش روش‌هاي ساده شامل درخت‌ تصميم، جنگل تصادفي، $K$-نزديك‌ترين همسايه و بخش روش‌هاي پيچيده‌تر شامل ماشين ‌بردار ‌پشتيبان و شبكه عصبي مورد مطالعه قرار گرفته‌اند. همچنين دقت اين روش‌ها بر روي مجموعه داده‌هاي مربوط به دانشجويان دانشگاه رازي از سال 1375 تا 1401 در مقطع كارداني و كارشناسي مورد بررسي و مقايسه قرار گرفته است. از روش‌هاي بررسي شده جنگل تصادفي بيشترين دقت پيش‌بيني را نتيجه داده است اما از لحاظ سرعت پاسخ‌دهي هزينه محاسباتي بالايي دارد. روش $K$-نزديك‌ترين همسايه از لحاظ دقت خيلي نزديك به روش جنگل تصادفي است با اين تفاوت كه زمان اندكي لازم است تا خروجي‌ها حاصل شوند.   

to the importance of its usage. One of the most important challenges in discussing theprogressive Type-II censored data is to determine the removal scheme. The removal schemecan be fixed or randomly selected according to a discrete probability distribution. Thisthesis considers the estimation problem for the two-parameter Pareto distribution underprogressive Type-II censoring with random removals, where the number of units removedat each failure time has a binomial distribution. The main focus of this study is on theBayesian estimates of Pareto distribution using Jeffery’s non-information and InformativePower Gamma distributions as priors for the unknown parameters under the squared errorand absolute error loss functions. Furthermore, the statistical performances of the obtainedestimators are compared with each other and with the maximum likelihood estimators.The comparisons have been done by Monte Carlo simulation. Finally, the E-Bayesian andhierarchical Bayesian estimations of the parameter derived from Pareto distribution arestudied and compared under different loss functions.  

In many applications, the data subject to inverstigation are in the form of location or geographical positions of some events in a specific region. In the present thesis, we are facing data related to location of corneal endothelium cells of 153 individual. Here, for proper analysis of this data, we have linked spatial point patterns to these images so that we can classify a group of very similar images into identical clusters based on clustering algorithms related to space point patterns. To investigate the cases of dissimilarity, the nearest neighbor distance function, empty space function, K-reply function, etc, have been used.

In analyzing big data, time of computations is increased, so in data mining algorithms cannot use all the data. Therefore, using sampling methods in big data set is a good solution.\\\\In statistical studies of multivariate populations, obtaining information over all variation range of variables is very important. Since it is difficult or impossible to select all data, the required information can be obtained by survey a subpopulation as a sample. In such cases, the appropriate sample can be selected by LPM2-kdtree method.\\\\Also, in big data analysis, selection bias is very important. In this thesis, in order to decrease the bias by using importance sampling a method is explained. Finally, in a numerical study on two real populations, the spatially balance of LPM2-kdtree and decreasing selection bias of the sampling design that uses importance sampling are evaluated.\\\\ \\textbf{Keywords:} {Big Data}, {Clustering}, {Data Mining}, {Inverse sampling}, {Knowledge Discovery}, {Non-probability sampling}, {Selection bias} . \\end{latin}

  The subject of classification is the one of the important issues indifferent sciences. The logistic regression is the one of the statistical methods to classify data in which the underlying distribution of the data is assumed to be known. Today, researchers in addition to statistical methods use other methods such as machine learning to classify data.  In this thesis, the decision trees C4.5, C5, CART, CHAID, and QUEST  are introduced,  and each of them is completely studied. Some ensemble learning algorithms such as random forest, Bagging, and Boosting in the field of supervised learning are also explained. Finally,  using five data sets, we compare the performance of these algorithms with respect to the accuracy measure.

   One of the fundamental issues in statistics is the modeling of random phenomena. Generally, statistical models are used to represent random structures, predicting future behavior of variables, deduction and extraction of information from data. In the meantime, the copula function as a model for multivariate and dependent observations has attracted the attention of many users in recent studies. In fact, an alternative way to model the dependency structure between multivariate data without imposing any assumptions on the marginal distributions based on the structure of the copula functions has been proposed which considers defects such as linear correlation coefficient, asymmetry and sequence dependence. Copula functions are functions to create a multivariate common distribution. Or, in other words, it establishes relationship between multivariate distribution functions and one-dimensional marginal distribution functions. These functions of the marginal distributions have a continuous uniform distribution over interval (0,1). In addition, copula functions are useful in obtaining dependency on both sides of the distribution by using the tail dependence. In this thesis, the selection of copula functions is performed using maximum likelihood method and prediction method. And the appropriate copula function on the Automotive and Metal Industry Stock Exchange data for years 88-96 based on the maximum likelihood estimation method and the Akaike information criterion as well as on the prediction method has been determined and used to provide optimal forecasts on the data.

همه ي ما ناراحتي انتظاركشيدن درصف را تجربه كرده ايم.علت اصلي تشكيل صف اين است كه تقاضا براي سرويس بيش ازامكانات سرويس دهي است. در دنياي امروز با توجه به پيشرفت تكنولوژي، سازمان ها در تلاش هستند كه از رقبا پيشي بگيرند و اين جز با برنامه ريزي دقيق و به كارگيري صحيح منابع و امكانات امكان پذير نيست. بنابراين مديران با توجه به پيچيدگي سيستم ها، بايد با استفاده از ابزارهاي مناسب مانند برنامه ريزي خطي، برنامه ريزي پويا، برنامه ريزي اعداد صحيح، شبيه سازي، تئوري صف و ... كه براي تحليل سيستم هاي وجود دارند، برنامه‌ريزي صحيحي انجام داده و از به هدر رفتن منابع جلوگيري كنند. . دراين تحقيق مفاهيم لازم براي يادگيري صف وصف بندي ونيز شيوه ي شبيه سازي مدل هايي ازصف بندي ارائه گرديده است.كليد واژه: سيستم صف بندي، تئوري صف، الگوي ورود متقاضيان،الگوي سرويس،نظم صف،ظرفيت يا گنجايش سيستم،تعدادمتقاضيان درسيستم،شبيه سازي   

   Normal 0 false false false EN-US X-NONE FA The weighted k out of n system is a one with n components that each component has a specific weight and it works if sum of its active components be at least k. A lot of researches and studies have been carried out around the properties of k out of n systems. This thesis investigates the reliability and some properties of these systems. One of these properties is the redundancy allocation that its result has been presented in the first part of this thesis. In the next part, the result of a weighted k out of n system with dependent components have been studied. Finally, k out of n system generalized to the weighted (k1, k2, …, km) out of n system and its result have been presented.

Our research is applied in terms of purpose. Because the proposed model lays solutions to improve the premium determination and generally improve the performance of insurance companies.We offer model forecasting methods to determine the premium rate,That detects data exploration and modeling. Among these methods, the accelerated gradient is a method in composite Poisson model. Since the main variables and interaction effects used in the models are, therefore, a tree accelerated gradient algorithm with the name TDboost offer visited. Also for data with a large zero accumulation The methods will be provided to make the premium forecast possible . First, we will discuss the definitions and concepts required in insurance science . So we introduce and examine the accelerated gradient tree model .In the third chapter, we implement a model for the survey of the database composite Poisson with insurance studies data.In the fourth chapter, we will analyze and compare non-parametric models using data sets, And finally, we will conclude our suggestions and conclusions.  

  ‏در آمار يكي از ابزار مهم براي تحليل داده ها در مدل هاي آماري برآورد پارامترها و انتخاب متغير مناسب است و روش هاي مختلفي براي آن وجود دارد. دو مورد از معروف ترين آن ها در حالت كلاسيك روش كمترين مربعات معمولي و روش بر‎‏آورد درستنمايي ماكسيمم است. اما در رگرسيون با بعد بالا‏، به علت وقوع مشكل بيش برآورد نمي توان از اين روش ها استفاده كرد‏، پس محقق سعي مي كند با كمك روش هاي انقباضي مانند رگرسيون جريمه دار اين مشكل را حل كند. در حالي كه آمار بيزي براي برآورد پارامترها از برآورد حالت پسين استفاده مي كند. زماني كه با رگرسيون با بعد بالا مواجه مي شود‏، تلاش مي كند كه اين مشكل را با استفاده از روش هاي   تنظيم بيزي (انقباضي بيزي) حل كند. اين روش ها تعداد متغيرهاي پيش بيني كننده و پيچيدگي مدل را كاهش مي دهند و برآورد پارامترها و انتخاب متغير ها را ساده تر مي كنند. بنابراين در اين پايان نامه اين روش ها را مورد بحث و بررسي قرار مي دهيم

   Variable selection is one of the most important topics in statistical modeling which is widely used in statistical applications. In this thesis, penalized regression models are used for selection important variables and in order to accelerate the estimation procedure of regression coefficients from partial likelihood of recurrent event data, the coordinate descent algorithm is applied. Using real longitudinal data from 230 patients with schizophrenia admitted to Farabi Hospital in Kermanshah from 01/01/1395 to 12/12/1397, each experienced more than one recurrence was able to select important variables. We have differentiated from the large number of covariate variables included in this data and finally fitted the models. Keywords: Longitudinal Data, penalty Regression, Partial Likelihood, Recurrent Event Data, Coordinate   Descent Algorithm

  Adaptive web sampling design is a flexible >In these designs, an initial sample is first taken, then the selection of the next units is based on thecompound distribution: that is, with a predetermined probability, the units are selected through thelinks that are connected to the previous sample, or a unit is selected randomly. In this thesis, this

  The importance of Kriging methods in geological studies is widely used and Determiningthe sample points is one of the most important questions in this research.in this thesis, theoptimal sampling in Kriging interpolation is studied using Spatial annealing algorithmsIntended sampling contrary to statistical inference, is not random. But it is purposivesampling method. Optimal sampling is a condition of sample points that optimizes thecriterion for determining the accuracy of interpolation.In simulation studies, differentcommunities have been investigated and based on the criteria of the empirical distributionfunction and etc. Samples with optimal position are specified

  در اين رساله، انواعي از سياست نگهداري براي پيشگيري خسارت­هاي(گاهاً جبران­ناپذير) ناشي از خرابي قطعات در حين كار كردن، مطالعه مي­شود. همانطور كه بيان شد شكست واحدها در زمان كار كردن ممكن است گران تمام شود. در مواردي كه با افزايش عمر، نرخ شكست افزايش مي­يابد، براي جلوگيري از خسارات، واحد را بايد قبل از آنكه خراب شود تعويض كنيم. سياست تعويض عمر، از پايه­هاي اصلي سياست نگهداري است كه براي جلوگيري از شكست يك واحد در زمان كار كردن است. در سياست تعويض عمر، قطعه در زمان شكست و يا زمان مشخص t تعويض مي شود اگر قطعه در زمان t در حال كار كردن باشد.مشخص است كه تعيين زمان t يكي از مسايل بسيار مهم در بحث سياست جايگذاري است.بارلو و پروشان(1965) ميانگين زمان شكست تحت سياست جايگذاري را به عنوان معياري از تاثير t معرفي نمودند.

  Determining the suitable premium for an insurer is one of the most important categories in the insurance industry. Inmostbonus-malussystems premiumbasedonthenumberofclaims Theclaimamountsarenot taken into accont. In this case, policyholders who had accidents with small or large claims are penalized unfairlyinthesameway. Ateventhepolicyholdersmayleavetheinsurancecompanytogetridoftheirbad history claims. In this thesis, in addition to the number of claims, the amount of claim is also considered. Also, in the malus zone, relative premiums softened by introducing and applying deductible  

  Optimal designs have an important role in designing the experiments and help the experimenter to do the experiment in a shorter time and with lower costs. In order to find the optimal designs, one has to consider the optimality criteria which is usually a function of Fisher Information Matrix. In the present thesis, the optimal designs for regression models with interval-valued data are obtained. These data are in fact, observations that are not accurately measurable and are reported as intervals. In this thesis, linear regression models fit these data and an optimal design for them is obtained.

  AbstractDiseasemapping refers to a set of statistical methods in which the incidence orprevalenceof a type of disease or death due to a specific cause within a geographicrangeis investigated . Consider the spatial area that has been compiled into severalsubsurfaceareas and the number of incidents occurring in the area under studyThederived spatial data is called spatial counting data The purpose of the diseasemappingis to estimate the relative risk of the incident in each of the sub-areas basedonthe data collected One of the most common models in disease mapping is theBYMmodel, which uses a randomized Gaussian mapping field (GMRF) to modeltherandom effects of sub-regions and correlations between space between sub-areaInthis thesis, the BYM model and Bayesian inference are described with the aid ofthe null cluster approximation method of the inla integral packet In the end,this modelis used to determine therelative risk of death from driving accidents in Kermanshah province  Keywords: diseasesmapping, spatial models, method using integratated nestedLaplace approximations(INLA), model BYM    

  We all have experienced the discomfort of waiting the queue.traffic or for paying tolls and ... .Themain reason for queuing is that demand for service is more than the service facilitties. Queuetheory is linked to factors such as queuing time,queue length,etc.With the expected properties ofthe flow of input to the system and service practices,it proposes an optimal system to reduce thedamage caused by queuing.In this thesis,after presenting the introduction and initial concepts, an invistigation of an unlimitedsource system and its prominent features,including the number of applicants in queue andsystem,waiting time,and so on will be done.In this model inputs have poisson distribution and servicetime exponential distribution.We then examine the bayesian queues M/M/1 and M/M/s,andwe see that there are some queuing features that are not mathematical expectation for them.Thenwe obtain the point estimate,distance and hypothesis test for Bayes systems and finally,we willsimulate what we have been studying at the end.

  چكيدهپديده انتظار كشيدن در صف با افزايش تراكم جمعيت و شهري شدن جامعه ، بيش از پيش گسترش يافته است هدف از اين پايان نامه،پيش بيني زمان انتظار هر مشتري در مدل صف M/M/S   است .در اين سيستم، تصميم گيرنده گان قصد دارند نتايج مفيدي را با ارائه دانش كافي در مورد سيستم صف بدست آورند.در اين پايان نامه براي مدلسازي صف M/M/S فرآيند زاد و مرگ ماركوفي را در نظر مي گيريم، نرخ   ورود ? و داراي توزيع پواسون و فاصله زماني بين دو ورود متوالي داراي توزيع نمايي و همچنين نرخ سرويس ? و داراي توزيع نمايي است .ما يكي از بانك هاي شهر كرمانشاه (بانك ملي) را انتخاب كرده تا عملكرد رفتار بانك با چند سرويس دهنده (باجه ) را مورد ارزيابي قرار دهيم . داده هاي مربوط به ورود و زمان سرويس هر مشتري در طول يك روز كاري بانك ( 6:30 صبح لغايت 12:30 بعد از ظهر ) يادداشت شده ، سپس پارامترهاي مدل صف M/M/S با محاسبات رياضي و نرم افزاري بدست آمد و با يكديگر مقايسه شدند و سپس تأييد مي شوند كه از دو روش نتايج بدست آمده برابرند.در پايان نيز به كمك شبيه سازي(فصل چهارم)پارامترهايي كه از مدل واقعي بدست آمده اند،برآورد مي شوند و مورد مقايسه قرار مي گيرند و نتايج حاصل به بانك داده شده و با ارائه راهكار مناسب به كاهش طول صف و زمان انتظار مشتريان در صف و سيستم مي پردازيم.كليد واژه ها : تئوري صف بندي در مدل M/M/S ، بانك ملي ايران ، توزيع احتمال ، شبيه سازي  

  The research on optimal reinsurance design has a long history for academicians and practitioners. Because it is an effective risk management tool for insurers. Depending on the chosen objective and constraints , there are many ways for optimal design of reinsurance.The primary objective of the thesis is to examine theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a numberof reinsurance models are examined and their optimal reinsurance treaties are derived. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the mostcommon risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer’s profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer’s empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.

  When determining the locating of the units with the largest number of variables studied (Hot spots), determining the most efficient  sampling method is important. Some ofthe methods employed in spatial communities are systematic sampling, stratifiedsampling method, and adaptive sampling method. In this thesis, theeffectiveness of various sampling methods including simple random sampling, systematicsampling, stratified sampling and cluster adaptive sampling for locating Hot spots have been studied.  

  Measuring and comparing risk in the insurance management process is essential, because of the risk measurement in banks, insurance companies and financial.The basis for desicion making is to allocate their resources.One way, the comparison based on some of the measure of the important risks and compare the risk with the stochastic order.In this dissertation, we propose a generalization of the increasing convex order to the multivariate setting to compare vectors of risks that accounts for both the marginal impacts and the dependence structures ofthe vectors. This generalization is suitable for comparing vectors with heterogeneous components andextends some well-known properties of the univariate increasing convex order. For example, comparisonsof vectors with the same copula can be characterized in terms of the multivariate tail conditionalexpectations introduced by Cousin and Di Bernardino. Also the multivariate extensions of the risk measures, tail conditional expectation and value at risk are presented and their invariance with respect to the univariate case are characterized.

The Study of the spatial pattern of trees in a forest stand has always gained attention among forestry researchers. Data on Spatial location of individual trees in a natural forest can present useful information on the distribution and structure of different forest species, as well as interaction between them. In the paper, data on spatial location of Iranian oak (Quercus brantii) in a 2 hectares plot in the zagros forests, Hasanabad area (west of Iran) were investigated. To this end, statistical methods in spatial point process, particularly widely used summary statistics like the pair correlation function and J function, were employed. Based on the results, there was a significant positive interaction (clustering) within Iranian oak species at spatial distances 2 to 6 meters, while no significant interaction was observed for other species.In addition, there was a significant interaction repulsion Iranian oak and other species.

Optimal ‎designs ‎as a‎ ‎tool, ‎which ‎help ‎researchers ‎to ‎predict ‎more ‎accurate ‎results, ‎has ‎been ‎commonly ‎considered ‎for ‎along ‎time. ‎Most ‎of ‎these ‎researches ‎are ‎based ‎on ‎the ‎Linear ‎models ‎with ‎normal ‎distribution ‎for ‎response ‎variable. ‎Another ‎assumption ‎which ‎has ‎been ‎considered ‎in ‎the ‎regular literatures, ‎is ‎the ‎independency ‎on ‎predictor ‎variables. ‎In ‎the ‎present ‎thesis, ‎we ‎study ‎Poisson ‎regression ‎model ‎as a‎ ‎special ‎case ‎of ‎generalized ‎linear ‎models. ‎Also ‎we ‎consider ‎some ‎cases ‎with ‎dependent‎ ‎predictor ‎variables. ‎‏‎$‎‎‎A-‎$‎optimal ‎designs ‎obtain ‎for ‎Poisson ‎regression ‎model ‎and ‎Poisson ‎ridge ‎regression ‎model. ‎We ‎also ‎calculate ‎ridge ‎parameter ‎based ‎on a‎ ‎new ‎method. ‎The ‎new ‎method ‎to ‎find ‎the ‎new ‎ridge ‎parameter, ‎compare ‎to ‎the ‎some ‎previous ‎methods.

‎Cox processes appropriate statistical models for cluster point patterns like trees in a forest location‎. ‎In the meantime‎, ‎log-Gaussian Cox processes for high flexibility in modeling and statistical analysis in a forest where trees are of most interest‎. ‎Considering the Bayesian approach can be integrated nested Laplace approximation method (INLA) for estimation and statistical inference about the parameters of a log-Gaussian Cox model was used‎. ‎INLA a quick‎, ‎yet thorough approach to Bayesian estimation of parameters of statistical models with a Latent Gaussian model (LGM)‎, ‎such as log-Gaussian Cox process models‎. ‎The INLA is a promising new technology for Markov chain Monte Carlo Bayesian inference without (MCMC)‎, ‎is also a definite alternative to this approach‎, ‎the main advantage of MCMC method to calculate the INLA is fast‎, ‎because calculations using Markov chain Monte Carlo is time-consuming‎. ‎In this thesis‎, ‎Bayesian inference for log-Gaussian Cox processes with INLA approach to examine and use it for modeling the location of trees in a forest‎.

  ‎In statistical study of spatial two-dimensional societies‎, ‎one of the purposes of which is preparing different plans‎, ‎collecting data from all area is of great importance‎. Since enumerating‎ all points a ‎wide‎ area is difficult and in some cases impossible‎, ‎then the required data should be collected only for a part of that area as the sample‎. ‎In a conventional and non-spatial population in which the location of the sample unit is not considered‎, ‎the main assessment criterion for sampling is efficiency of the estimator‎. ‎In sampling two-dimensional areas‎, ‎in addition to efficiency and estimators precision‎, ‎well-ballance of all the area is considered as well with due consideration to sampling methods in two-dimensional ‎population‎‎, ‎in this thesis‎, the relate ‎sampling methods are studied‎, also their well-spread‎, ‎and efficiencies are measured.

In many from life ‎testing and reliability ‎studies, the experimenter may not always obtain complete information on failure times for all experimental units. for Example, individuals in a clinical trial may drop out of the study, may have to be terminated for lack of funds or in an industrial experiment, units may break accidentally. ‎Therefore, one has to remove some units prior to failure for saving time and cost associated with testing. Data obtained from such experiments are called censored. The most common censoring schemes are type I and type II. The Type I and Type II censoring schemes have major deficiency in that they only do not allow removal of units at points other than the terminal point of the experiment. Due to experimenter use a versatile scheme of censoring called progressive.‎This thesis has been focused on the scenario of progressive Type II censoring. A problem associated with this scheme is that the total testing duration might be unacceptably long. To address this issue, a hybrid variant of the ‎progressive ‎‎censoring scheme was proposed in which imposing a time limit T on the test. Although this hybrid ‎progressive ‎‎censoring scheme controls the total testing duration not larger than T, it is possible that the effective sample size is very small or even zero in which usual efficient statistical inference may not be feasible. To strike a balance between the ‎total ‎testing ‎time ‎and ‎the ‎efficiency ‎in ‎statistical ‎inference, ‎Ng ‎et.al ‎(2009)‎ proposed an adaptive Type II progressive censoring scheme.In this thesis influential methods for progressive Type II censoring and adaptive Type II progressive censoring under some statistical distributions are studied. We ‏‎obtain‎ both maximum likelihood estimators, approximate maximum likelihood estimators and observed information matrix for the unknown parameters. We simulated values of the estimates parameters, a comparison of the values variance and covariance of the estimators with those obtained from the corresponding observed information matrix and coverage probabilities for pivotal quantities based estimators. Various interval estimation methods for the unknown parameters such as asymptotic confidence intervals with both observed information matrix and fisher information matrix, percentile bootstrap and bootstrap-t confidence intervals are obtained. Then these methods are compared in terms of their expected lengths and coverage probabilities using simulation.

  We all have experienced the discomfort of waiting in queue, or to pay the toll roads in traffic, sitting in the car waiting; to pay for items bought in stores and we will remain in government offices’ queue. We, as customers, generally do not like this kind of waiting and managers also do not like seeing us waiting in the queue, because these queues may have cost for them.The main reason of forming queue is that the demand for service is more than service’sfacilities. Queuing theory by linking factors such as waiting time in the queue, queue length and etc. considering the given properties login and service practices,formsan optimized designsystem to reduce the damage caused by queues. In this thesis, after the introduction and basic concepts, we study queuing model Mb / M / 1 withreviewPoisson arrival rate that is fixed with customers to bulk the distribution server is exponential. And then non-Markov model M / G / 1 that is the customer’s time service overall distribution function.Then study such components such as queue length, number of customers in the system and the system busy period. At last, we study   Mx/ G / 1 queue model to conclude and waiting time in the system and period of unemployment and employment, and in steady state in the queue. And finally, we study their generating functionin a steady state.Keywords:   Bulk Queue, Steady State, entropy, Breakdown, Supplementary, Unreliable, Queue Size